MinT - Information on Result #1017204

Information on Result #1017204

Linear OOA(49²⁸, 40393, F₄₉, 3, 8) (dual of [(40393, 3), 121151, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49⁶, 1176, F₄₉, 3, 4) (dual of [(1176, 3), 3522, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(49⁶, 2352, F₄₉, 4) (dual of [2352, 2346, 5]-code), using
  - 1 times truncation [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
    - a code by Danev and Olsson [i]
linear OOA(49²², 39217, F₄₉, 3, 8) (dual of [(39217, 3), 117629, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(49²², 117651, F₄₉, 8) (dual of [117651, 117629, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(49²², 117652, F₄₉, 8) (dual of [117652, 117630, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(49²², 117649, F₄₉, 8) (dual of [117649, 117627, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(49¹⁹, 117649, F₄₉, 7) (dual of [117649, 117630, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(49⁰, 3, F₄₉, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.